It's 3 pieces. Pull off the two outer sleeves, then slide the inner sleeve out. You should probably replace the DU bushing at the same time. If the inner piece slides out easily, the DU needs to be replaced. You can get a new DU from your LBS, or order a roller bearing kit from enduro fork seals.
A table vice is handy for the work.
Based on your posted skills and tools it ay be best to have the LBS do it.

It's 3 pieces. Pull off the two outer sleeves, then slide the inner sleeve out. You should probably replace the DU bushing at the same time. If the inner piece slides out easily, the DU needs to be replaced. You can get a new DU from your LBS, or order a roller bearing kit from enduro fork seals.
A table vice is handy for the work.
Based on your posted skills and tools it ay be best to have the LBS do it.

I have the outer caps off in the pic. The remaining thing is called "DU?" What does this stand for.

I want to know how to get the DU out. Once I have it out, how do I get in back in and centered once it goes back in.

The 3rd piece we'll call the pin. There is no trick to getting it out. It should not come out easily.
The DU is a bushing inside the shock eyelet, it's what the pin slides into. It's a wear and tear part that needs to be replaced when worn.
To get the pin out you will need to get creative. Usually a homemade press will work.
Get a long and thin bolt with a nut and some washers.
Get a piece of pipe a bit longer than the pin length, and wide enough that the pin will fit inside.
Get a socket with a slightly smaller diameter than the pin.
Assemble it all so the socket is on one side if the pin, the pipe on the other, and the bolt and washers hold it all together. Then tighten the bolt to press out the pin. Same process can be used to put it back together.
Do not grab the pin with pliers, it will gouge it and cause you problems on reassembly.
Changing the DU is a similar process. The DU is. Thin metal sleeve that it pressed into the shock eyelet and usually has an orange liner that wears away where the pin rubs on it.

Why are you servicing the shock, something wrong or just regular maintenance?